Such high power electric machines, as turbogenerators are cooled due to high heat generation in operation. In the following the concept of gaseous cooling of the rotor of the electric machine is disclosed, as an example cooling by medium air. In particular, the coils comprising windings wound around the rotor to induce a magnetic field in the rotor core are to be cooled or ventilated. To this end cooling paths are designed at the end of the coils along which the cooling gas flows. It may be advantageous to specify these coolings paths and enhance the cooling efficiency.